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DeWayfarer Isee. Thankyou for explaining it.
The system I had, and all the books I've seen, don't divide it quite like that. Instead they assume a continuum advancing via different forms of equation, to calculus (and beyond, at University level). I have seen text-books dedicated to calculus from introducing it, and other concentrating on advanced pure algebra, but not intended as subjects all on their own.]
I have an early-1960s school maths text-book and it does have hints on social expectations of their time. It was written by a teacher, I think the headmaster, of an English "public school" (by the English definition) whose pupils were from well-off families and groomed for careers in high-pay areas like finance, the Law and the military. So the sections on Percentages concentrate heavily on money: loans, debts, and stocks and shares!
I forget when I was introduced to percentages, in my Local Education Authority (State system) schools. Their use in money may have been the main examples if only because in later life understanding money is a key skill for everyone.
Algebra gained a notoriety because less-numerate puplis (including me!) found their abstract nature hard to handle, but also perhaps because we were rarely given any idea of its meaning and purposes - just how to "do" it. The nearest that the equation exercises came to real-life were timing the cyclist passing a walker in the opposite direction, or more realistically, two trains in opposite directions passing each other.
It may have helped if once we'd passed the introductory phase of basic algebra as arithmetic in general form, then using real formulae from science and engineering. Even if not understanding their purposes in detail, it would at least show that, yes, lots of real people really do use algebra for real work! (Like Ohm's Law.)
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I met that vagueness in the course I followed in my forties. This was the standard middle-school maths (for pupils in early to mid-teens). Some was simply revision for me but it introduced a very strange beast indeed - The Matrix.
Although at this level it was merely how to add or multiply boxes of simple numbers and manipulate odd things with non-intuitive names, I found it totally baffling because they were taught as having nothing to do with any other branch of mathematics, and no reference to any real-world uses. A scientist told me the analytical software she uses for her work, relies on matrices, but that is in an extremely advanced, specialist area of physics and engineering!
So I never understood matrices even at introductory level, only how to add two boxes of simple numbers, and have never personally met them in real life .
